Simplify [{38 - ( - 6)} × {9 - (8 - 1)}] ÷ [4 × {6 + ( - 4)}].

To simplify the given numerical expression, we will follow the order of operations (BODMAS/PEMDAS rule), which dictates that we perform operations inside brackets (parentheses, braces, and brackets) first, moving from the innermost to the outermost, followed by multiplication and division (from left to right).

The given expression is:
$\left[\right\{38-(-6)\}\times \{9-(8-1)\left\}\right]÷[4\times \{6+(-4)\left\}\right]$

Let's simplify the expression step-by-step by breaking it down into the numerator part (before the division sign) and the denominator part (after the division sign).

Step 1: Simplify the first term in the numerator
Consider the term $\{38-(-6\left)\right\}$:
Subtracting a negative number is equivalent to adding its positive counterpart:
$38-(-6)=38+6=44$

Step 2: Simplify the second term in the numerator
Consider the term $\{9-(8-1\left)\right\}$:
First, simplify the innermost parentheses:
$8-1=7$
Now substitute this back into the term:
$9-7=2$

Step 3: Combine and simplify the entire numerator bracket
Now we multiply the simplified values from Step 1 and Step 2:
$[44\times 2]=88$

Step 4: Simplify the denominator bracket
Consider the term $[44\times 2]÷[4\times \{6+(-4)\left\}\right]$ and let's work on the right side: $[4\times \{6+(-4)\left\}\right]$.
First, simplify the innermost braces:
$6+(-4)=6-4=2$
Next, multiply this result by 4:
$4\times 2=8$

Step 5: Perform the final division
Now, divide the simplified numerator (from Step 3) by the simplified denominator (from Step 4):
$88÷8=11$

Therefore, the simplified value of the expression is 11, which matches Option 11.